Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3,4), (7,8)
A) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$
B) $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 8$
C) $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$
D) $( x + 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 340$
E) $( x - 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 340$

Question

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is $\left( \frac{3+7}{2}, \frac{4+8}{2} \right) = (5, 6)$. The radius can be found by calculating the distance between one endpoint and the center, which is $\sqrt{(7-5)^2 + (8-6)^2} = \sqrt{4 + 4} = \sqrt{8}$. Thus, the equation is $(x - 5)^2 + (y - 6)^2 = 8$.

Write the Standard Form of the Equation of the Circle (x−5)2+(y−6)2=8( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8(x−5)2+(y−6)2=8

Write the Standard Form of the Equation of the Circle $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$